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Redownloaded 2 times
Tried a different mac
Tried changing the format to Apple Partition Map
None of these worked, I am going to try DiskMaker and keep my fingers crossed. If you have any suggestions just post them. Also can some one please post the code to install it from a location on the desktop not the Applications folder. Thanks!

You could plug it in, hit "Ignore", open "Disk Utility", and attempt to "Repair" the disk. Otherwise, try to initialize the disk and copy the folder contents.
P.S. Just as a side note, I would recommend using an external hard drive(SSD or HDD) to run OS X, since it would operate a little faster.

For me it was a permission issue. I copied it to Desktop and ran this command and it fixed the problem:
sudo chown yourusername -Rv ~/Desktop/Install\ OS\ X\ El\ Capitan\ Public\ Beta.app
Copying to Desktop might not even be needed.

I tried many things talked about here and on other top Google searches:
Redownloaded (three times)
Tried moving the .app to Desktop
Changed permissions of .app
Verified the .dmg with hdiutil
Used different Mac
Eventually got it to work by using a different USB flash drive. My original USB was a 16 GB Kingston, the second I tried that also didn't work was ...

I was having this too. I finally had success by copying the install app/folder from /Applications to the desktop. Once there the "mount of outer dmg" message was no more, despite using the same command (other than the appropriate path changes). Might not be the solution for everyone, but it did work for me.

What you're trying to do is verify the integrity of the electronic software delivery (ESD) image. But you somehow got it wrong, it should look as follows:
hdiutil verify /Applications/Install\ OS\ X\ El\ Capitan\ Public\ Beta.app/Contents/SharedSupport/InstallESD.dmg
For me the integrity is checked ok, still I have the same error as you:
Mount of outer ...